MN || OP in O0 mMQ = 2(mNP) Given: Prove: M. 2.

Q: Suppose we have some approximation N(h) to M, and we know that N(h) = M + C¡h+ C2h² + C3h³ +0 (h*) .…

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Q: Using the Green's 2nd identity, prove that for 2-D Neumann exterior problems, O(In r) 09 Inr-0 dl .…

A: Consider the Green's second identity, ∭Du∆v-v∆udv=∬∂D=u∂v∂n-v∂u∂nds From the equation consider the…

Q: .rdx dy Prove that (a) (b) (8)

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Q: 25.In solving r In(In x) dx , which substitution should be used? O A. u = In(In æ) In a O B. U = Oc.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: While evaluating the approximate value of 1' dr, using Trapezoidal rule, taking h = 0.5, the N is =.…

A: Use formula for N

Q: In (T/e) ( (2- sec?x)eme sec³x sec (зА - х) -dx to be integrable using the formula и" du? ? What…

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Q: Evaluate * ISS 9z dV E where E is enclosed by z = x? + y? and z = 1 4JT O 3T O 27 ол

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Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

Q: Find the general solution of the given variable separable egm atim. dy *+ ay? (2) %3D

A: Given :dydx=e3x2+4y2

Q: eln (R/c) secx - sec?x)" sec(34 – x) "du?? dx to be integrable using the formula What should be the…

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Q: Pn 1995 Hhe moose papulalion n MeaSured to be 1900.TTBa, 1994, Hbe Was, eaSuned agaio to be Uu400.1f…

A: Given query is to find the formula for the function P.

Q: of the hghset of cheryt the t y temthe 2M percetaof the tres aea dy tn than ees hae ate your

A: Given that  The histogram data of heights of cherry trees. We write the given data in frequency…

Q: ue of the det e 16 is

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Q: The work W (in N • m) in winding up a 60-m cable is W = (1600 – 7x)dx. Evaluate W.

A: The given integral is ∫0601600-7xdx

Q: i =r+ 1+1 1le n de bifureation? on?

A: This is a problem of Dynatic Model, stability Analysis.

Q: By using Trapezoidal rule, the value of "h" in evaluating ((x² – 2x +1)dx, by taking 8 subintervals…

A: The value of h to evaluate the integral  is 0.25 option (a) is true.

Q: 3. Find x in ДPOR. R 12 О 13 О 15 О 16 O v60

A: We have to find value of x

Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: The DE : y = e-/Y is seperable Select one: O True O False on

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Q: QUESTION The minimum value of n required to approximate xedx by composite Trapezoidal rule with an…

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Q: The largest interval for which the IVP : (In(e* – e²)) y' + y = 1, y(5) = 0 х —6 has a unique…

A: We need to find the largest interval for which the given IVP has the unique solution.

Q: What is tanh (Ei) O V3 V3i O 13

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Q: EX Use Euler's method ( modified) to approx; mat e y' = x+y for yC1) = 1; h=o.1,13X<z withe aecuracy…

A: We Use here Euler's Modified Method to find the solution.

Q: Q: Prove the trans ferm; formula's by definition of Lapia (Dirac Delta fauncden) %3D

A: A delta function is defined as δ(t-a)=0     for t≠a∞   for t=a      . The fundamental property of…

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- 2* + 20z – 96z?…

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Q: Change the order of integration and hence evaluate o Sa ²(xy)dydx.

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Q: The value of c of fo-2- in the iterval .D such that rio--E) OA 3 OB. -3 OC 3 O0. 3-

A: c = 3explanation is given in below step

Q: O Evaluate the foll owing in tegrals: Ins 2x+y (Sinztcany) dx dy In2 e dydx JA ROSISu, Isys2

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

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Q: dy 3 (113) _1) dri Ber roullis Solve this by using caruation. %3D

A: The equation is given by: dydx=31313-1 Assume x=1,y=3 to get: dydx=yxy13-xdydx+xy=xy14 Which is a…

Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

A: This question is related to definite integration, we will solve it using given information.

Q: dy is then da In a If y = cosh r

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Q: ydy 4. S (1 + 3²) ² 4

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Q: Find the sum of (arctan(n + 1) – arctan(n)) if exists. Lütfen birini seçin: a. b. 3 2 d. e.0 DOO

A: Given- ∑n=1∞arctann+1-arctann To Find- The sum of the above expression.

Q: E valuate the Following Integral 2+7sin z z 2. COS Z

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Q: With integration by parts, J udv · Judv = UV - O True O False

A: Solve the following problem

Q: b) sol v e in e Iknear di tteren tiaı hrst oroer equanon dy 2. り = n2 cosh cen), when り (1)

A: The given differential equation: dydx-2xy=x2 coshex ;          y(1)=0

Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: 10. Given: YT = YP, LC = LR, Proof ZT= LP Prove: CT = RP R

A: Consider

Q: Apply Green's Theorem to evaluate the integral O(6y dx + 6x dy), where C is the triangle bounded by…

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Q: UCe the Vmit de fi miおもn of rhc aefrile へとgral, im ; fcxi)x - 5fしょsdx」 to prove hat ハう fex) dx= -…

A: Prove ∫abf(x)dx=-∫baf(x)dx using the limit definition of the definite integral as follows. By limit…

Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: 8) The integral |4* dx is equal to 5x 5x 5x - +C C. In 5 А. -+C In 4 В. +C 5in4 D. +C 4 In5

A: Given ∫45x dxSubstitute u=5x → dudx=5→dx=15du=15∫4u duNow solving ∫4u duApply Exponential rule: ∫au…

Q: The sum of Hthe first S=3n²+4a fFinal+he li mit an is nlmits ofar plogression an arthmctic

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Q: In (x le) (2– sec²x)elmtafcsec?x sec(3A – x) - dx to be integrable using the formula 'du? What…

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Q: Evculucte the ntegre ree)dt where re =secttleH, tine TNt C 2

A: The given function is